Support: Difference between revisions

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A [[regular temperament]] is '''supported''' by an [[equal temperament]] that makes all of its [[comma]]s [[vanish]].<ref>The original definition of support in this RTT sense was given by [[Gene Ward Smith]] in [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13967], "Suppose T is a wedgie, and v is an equal temperament val. Then v supports T if and only if T^v = 0."</ref> The equal temperament thus '''supports''' this temperament, or equivalently stated, the equal temperament ''is a temperament of'' this temperament, in the same sense as a temperament is a temperament of [[just intonation]].

A [[regular temperament]] is '''supported''' by an [[equal temperament]] that makes all of its [[comma]]s [[vanish]].<ref>The original definition of support in this RTT sense was given by [[Gene Ward Smith]] in [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13967], "Suppose T is a wedgie, and v is an equal temperament val. Then v supports T if and only if T^v = 0."</ref> The equal temperament thus '''supports''' this temperament, or equivalently stated, the equal temperament ''is a temperament of'' this temperament, in the same sense as that any temperament is a temperament of [[just intonation]].

For example, [[22edo|22-ET]] supports [[pajara]], because pajara makes [[225/224]] and [[64/63]] vanish, and so does 22-ET. The supporting temperament will make at least one additional comma vanish; in this example, 22-ET makes [[245/243]] vanish.

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	A [[regular temperament]] is '''supported''' by an [[equal temperament]] that makes all of its [[comma]]s [[vanish]].<ref>The original definition of support in this RTT sense was given by [[Gene Ward Smith]] in [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13967], "Suppose T is a wedgie, and v is an equal temperament val. Then v supports T if and only if T^v = 0."</ref> The equal temperament thus '''supports''' this temperament, or equivalently stated, the equal temperament ''is a temperament of'' this temperament, in the same sense as a temperament is a temperament of [[just intonation]].		A [[regular temperament]] is '''supported''' by an [[equal temperament]] that makes all of its [[comma]]s [[vanish]].<ref>The original definition of support in this RTT sense was given by [[Gene Ward Smith]] in [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13967], "Suppose T is a wedgie, and v is an equal temperament val. Then v supports T if and only if T^v = 0."</ref> The equal temperament thus '''supports''' this temperament, or equivalently stated, the equal temperament ''is a temperament of'' this temperament, in the same sense as that any temperament is a temperament of [[just intonation]].

	For example, [[22edo\|22-ET]] supports [[pajara]], because pajara makes [[225/224]] and [[64/63]] vanish, and so does 22-ET. The supporting temperament will make at least one additional comma vanish; in this example, 22-ET makes [[245/243]] vanish.		For example, [[22edo\|22-ET]] supports [[pajara]], because pajara makes [[225/224]] and [[64/63]] vanish, and so does 22-ET. The supporting temperament will make at least one additional comma vanish; in this example, 22-ET makes [[245/243]] vanish.